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Simplifying 3.25 = -0.2x2 + 1.75x + 7 Reorder the terms: 3.25 = 7 + 1.75x + -0.2x2 Solving 3.25 = 7 + 1.75x + -0.2x2 Solving for variable 'x'. Combine like terms: 3.25 + -7 = -3.75 -3.75 + -1.75x + 0.2x2 = 7 + 1.75x + -0.2x2 + -7 + -1.75x + 0.2x2 Reorder the terms: -3.75 + -1.75x + 0.2x2 = 7 + -7 + 1.75x + -1.75x + -0.2x2 + 0.2x2 Combine like terms: 7 + -7 = 0 -3.75 + -1.75x + 0.2x2 = 0 + 1.75x + -1.75x + -0.2x2 + 0.2x2 -3.75 + -1.75x + 0.2x2 = 1.75x + -1.75x + -0.2x2 + 0.2x2 Combine like terms: 1.75x + -1.75x = 0.00 -3.75 + -1.75x + 0.2x2 = 0.00 + -0.2x2 + 0.2x2 -3.75 + -1.75x + 0.2x2 = -0.2x2 + 0.2x2 Combine like terms: -0.2x2 + 0.2x2 = 0.0 -3.75 + -1.75x + 0.2x2 = 0.0 Begin completing the square. Divide all terms by 0.2 the coefficient of the squared term: Divide each side by '0.2'. -18.75 + -8.75x + x2 = 0 Move the constant term to the right: Add '18.75' to each side of the equation. -18.75 + -8.75x + 18.75 + x2 = 0 + 18.75 Reorder the terms: -18.75 + 18.75 + -8.75x + x2 = 0 + 18.75 Combine like terms: -18.75 + 18.75 = 0.00 0.00 + -8.75x + x2 = 0 + 18.75 -8.75x + x2 = 0 + 18.75 Combine like terms: 0 + 18.75 = 18.75 -8.75x + x2 = 18.75 The x term is -8.75x. Take half its coefficient (-4.375). Square it (19.140625) and add it to both sides. Add '19.140625' to each side of the equation. -8.75x + 19.140625 + x2 = 18.75 + 19.140625 Reorder the terms: 19.140625 + -8.75x + x2 = 18.75 + 19.140625 Combine like terms: 18.75 + 19.140625 = 37.890625 19.140625 + -8.75x + x2 = 37.890625 Factor a perfect square on the left side: (x + -4.375)(x + -4.375) = 37.890625 Calculate the square root of the right side: 6.155536126 Break this problem into two subproblems by setting (x + -4.375) equal to 6.155536126 and -6.155536126.Subproblem 1
x + -4.375 = 6.155536126 Simplifying x + -4.375 = 6.155536126 Reorder the terms: -4.375 + x = 6.155536126 Solving -4.375 + x = 6.155536126 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.375' to each side of the equation. -4.375 + 4.375 + x = 6.155536126 + 4.375 Combine like terms: -4.375 + 4.375 = 0.000 0.000 + x = 6.155536126 + 4.375 x = 6.155536126 + 4.375 Combine like terms: 6.155536126 + 4.375 = 10.530536126 x = 10.530536126 Simplifying x = 10.530536126Subproblem 2
x + -4.375 = -6.155536126 Simplifying x + -4.375 = -6.155536126 Reorder the terms: -4.375 + x = -6.155536126 Solving -4.375 + x = -6.155536126 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.375' to each side of the equation. -4.375 + 4.375 + x = -6.155536126 + 4.375 Combine like terms: -4.375 + 4.375 = 0.000 0.000 + x = -6.155536126 + 4.375 x = -6.155536126 + 4.375 Combine like terms: -6.155536126 + 4.375 = -1.780536126 x = -1.780536126 Simplifying x = -1.780536126Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.530536126, -1.780536126}
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